To resolve the issues (ii) and (iii), a close connection [1]} between color confinement in the large-\(N\)  gauge theory and Bose-Einstein condensation [2]} plays a crucial role.
The canonical partition function of gauge theory with gauge group \(G\)  at temperature \(T\)  is
\(Z(T)=\frac{1}{{\rm vol}(G)}\int _G dg{\rm Tr}(\hat{g}e^{-\hat{H}/T}),\nonumber \) 
